1. Ratio & Equivalent Ratios
A ratio is used to describe how two quantities are related.
For example, we might say that orange squash is to be mixed with water in a ratio
of 1:6.
This means that for every 1 part squash, there will need to be 6 parts of water.
If there was 100ml of squash, there would be 600ml of water. Another common
example of a ratio is a map scale. A particular map scale might be 1:50,000.
In this case it means that 1cm on the map represents 50,000cm in "real-life".
50,000cm = 500m = 0.5km, so 1cm on the map represents half a kilometre. 2cm
would therefore represent 1km.
Finding equivalent ratios
The ratio of squash to water in the example above was 1:6, but this could be written as
100:600, or 20:120, or 5:30.
These ratios are equivalent because they have the same meaning - the amount of water
is six times the amount of squash.
You can find equivalent ratios by multiplying or dividing both sides by the same
number. This is similar to finding equivalent fractions. Some examples of finding
equivalent ratios are shown on the right. All the ratios in the diagram are equivalent.
Writing a ratio in its simplest form
A ratio is in its simplest form when both sides are whole numbers and there is no
whole number which both sides can be divided by. In the example opposite, 1:6 is the
simplest form of the ratio.
To write a ratio in its simplest form, keep dividing both sides by the same number
until
you can't go any further without going into decimals.
Example: write 160:240 in its simplest form
160:240
40:60
(divide both sides by 2)
20:30
(divide both sides by 5)
4:6
(divide both sides by 2)
2:3
A
(divide both sides by 4)
SIMPLEST FORM
